Explosions and gunfire reported as armed men kill at least one student and injure 14 more inside campus.

At least one student has been killed after armed men attacked the campus of the American University of Afghanistan in Kabul, according to an official and a student.

About 14 more people were also wounded in the incident on Wednesday evening, Mohammad Saleem Rasouly, the head of Kabul's hospitals, told the Reuters news agency.

"Several gunmen attacked the American University in Kabul and there are reports of gunfire and explosions," the official said on Wednesday.

"[The attackers] are inside the compound and there are foreign professors along with hundreds of students."

Dozens of soldiers cordoned off the area after the attack started on Wednesday evening, when the elite private university is usually packed with students, many of them working professionals doing part-time courses at the facility.

Ahmad Shaheer, a student at the university, told the Reuters news agency that he was trapped inside the university.

"We are stuck inside our classroom and there are bursts of gunfire," he said.

No group has so far claimed responsibility for the attack, which comes as the Taliban step up their summer fighting season against the Western-backed Kabul government.

The attack came after two professors at the university - an American and Australian - were kidnapped in the heart of the capital earlier this month, the latest in a series of abductions of foreigners in the conflict-torn country.

The management of the elite American University of Afghanistan, which opened in 2006 and caters to more than 1,700 students, was not immediately reachable for comment.